Engineering Board Exam Reviewer · Linear First-Order Differential Equations · medium

Find the general solution of dy/dx-y/x=x2 for x>0.

1. y = C x + x33
2. y = C x + x32
3. y = C/x + x32
4. y = C x + x3

Answer

B. y = C x + x32

Solution

The integrating factor is 1x: d/dx≤ft( yx )=x yx=x2/2+C y=x3/2+Cx.

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